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We determine critical parameter sets for transitions from gradual toexplosive synchronization in coupled oscillator networks with higher-ordercoupling using self-consistency analysis. We obtain analytic bifurcation valuesfor generic symmetric natural frequency distributions. We show thatnon-synchronized, drifting, oscillators are non-negligible, and play a crucialrole in bifurcation. As such, the entire natural frequency distribution must beaccounted for, rather than just the shape at the center. We verify our resultsfor Lorentzian and Gaussian distributed natural frequencies.

Universal bifurcations to explosive synchronization for networks of coupled oscillators with higher-order interactions